Showing papers on "Paris' law published in 1974"
Book•
01 Jan 1974TL;DR: In this paper, the authors proposed a method to detect cracks in a crack-penetrization model, based on the Griffith criterion, which is used to detect the presence of a crack at a crack tip.
Abstract: I Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 "Leak-bcfore-break" criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.
2,539 citations
Journal Article•
TL;DR: In this article, the second phase of a study intended to provide reliable information on fatigue behavior of steel bridge members, and an extensive investigation of fatigue effects in welded steel beams, which formed the basis for recommendations for revision of the fatigue provisions of the AASHP Standard Specifications for Highway Bridges.
Abstract: This research (which is the second phase of a study intended to provide reliable information on fatigue behavior of steel bridge members), and an extensive investigation of fatigue effects in welded steel beams, which formed the basis for recommendations for revision of the fatigue provisions of the AASHP Standard Specifications for Highway Bridges. A hundred and fifty seven steel beams and girders were fabricated and tested to define the fatigue strength of various structural details, including stiffeners and attachments. Stress range was observed for nearly all the variation in cycle life for all stiffener and a attachment details examined in this study. For purposes of design the the fatigue strength of ASTN A514 steel rolled beams was found to be about the same as A36 and A441 steel rolled beams. The stress range-cycle life relationship described the fatigue strength for all three grades of steel. The beam bending stress range at the held toe termination was found to dominate the fatigue strength of full-depth stiffener details welded to the web alone. The bending stress range at the stiffener-to-flange weld defined the strength for stiffeners welded to the web and the flanges. For design purposes, the same fatigue strength values are applicable to transverse stiffeners welded to the web and the tension flange. The allowable bending stress range at the termination of the flange weld toe is the same as for stiffeners welded to the web alone. The magnitude of shear need not be considered when determining the allowable bending stress range for fatigue of full-depth stiffeners welded to the web alone. The welding of transverse stiffeners to the tension flange, the addition of new design categories to the AASHO specifications, fatigue crack growth, and the attachment of diagonal bracing to transverse stiffeners are other aspects which were studied. The empirical exponential model relating stress range to cycle life provided the best fit to the test data. A theoretical stress analysis based on the fracture mechanics of crack growth confirmed the suitability of the empirical regression models. The theoretical analysis also provided a means of rationally explaining the observed behavior and permitted the effect of other variables such as plate thickness and initial crack size to be examined in a rational manner.
161 citations
TL;DR: In this article, it was shown that crack closure occurs only when the stress intensity conditions were reduced to below the minimum stress intensity level (KM I N) for the previous fatigue cycles.
125 citations
TL;DR: In this paper, the application of acoustic emission to the detection of fatigue-crack propagation in 7075-T6 aluminum and 4140 steel is investigated, and the relationship between crack-growth rate, cyclic stress-intensity factor, load-cycling rate and observed acoustic-emission behavior is presented.
Abstract: The application of acoustic emission to the detection of fatigue-crack propagation in 7075-T6 aluminum and 4140 steel is investigated. The relationship between crack-growth rate, cyclic stress-intensity factor, load-cycling rate and observed acoustic-emission behavior is presented. Crack-growth rates of less than 10−6 in./ cycle could be detected, and acoustic-emission counts per cycle were shown to be closely related to the energy released by crack extension per cycle. A quantitative relationship for the threshold conditions for detection of fatigue-crack growth is presented which agrees with experimental test results. The results also showed that fatigue-crack growth occurs in an accelerating and decelerating manner, even though the stress-intensity range remains uniform, and that the count rate posses through a peak that is believed to be associated with a plane strain-plane stress transition. The effects of instrumentation sensitivity and frequency bandpass are also investigated. The results obtained indicate that acoustic-emission techniques should be suitable for in-service monitoring of a variety of cyclically loaded structures, even in the presence of high background noises.
122 citations
TL;DR: In this paper, a two-stage model for structure sensitive crack growth is proposed, where the transition from structure sensitive to structure insensitive can be correlated with the attainment of a critical value of the reverse plastic zone size equal to the α grain size of the microstructure in question.
115 citations
01 Jul 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the influence of microstructure on the strength, fracture toughness and low cycle fatigue behavior of 17-4 PH stainless steel has been examined, and it was shown that fracture toughness increased with increasing strength level and humidity but were not a function of toughness level.
Abstract: The influence of microstructure on the strength, fracture toughness and low cycle fatigue behavior of 17-4 PH stainless steel has been examined. Aging hardening involves initial formation of coherent copper-rich clusters which transform to incoherent fee ∈-copper precipitates upon further aging. The changes in strength level and strain hardening rates observed during aging are consistent with previously suggested models for precipitation hardening based on differing elastic moduli. The fracture toughness and fatigue crack growth rates were shown to be a function of microstructure and environment. At equivalent strength levels overaging resulted in a higher fracture toughness than did underaging. The fatigue crack growth rates increased with increasing strength level and humidity but were not a function of toughness level. Attempts to correlate the fatigue crack growth rates with monotonie tensile properties were unsuccessful. However when final failure obeyed a critical strain criteria, the fracture toughness behavior could be reasonably described and related to preferential void nucleation and growth at δ-ferrite-matrix interfaces.
108 citations
01 Feb 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, the authors proposed a mechanism for the structure sensitive mode of fatigue crack growth in vacua of 1.33 mN m-2, on Ti-6 A1-4V, at growth rates of 10-7 to 10-4 mm/cycle.
Abstract: Fatigue crack propagation studies in vacua of 1.33 mN m-2, on Ti-6 A1-4V, at growth rates of 10-7 to 10-4 mm/cycle have shown that a threshold for growth exists at ‡K values of 6.3 to 7.6 MN m-3/2. The value of the threshold level is microstructure dependent, but growth above this value was structure insensitive according to both growth rates and fracture surface observations. Some slow (≈ 10-8 mm/cycle) crack extension was observed below the threshold values but prolonged cycling reduced the growth rate to a vanishingly small level. Fracture surface observations indicated that growth in this region was microstructure sensitive. Comparison with previously performed air work on the same material showed that while structure insensitive growth rates in vacuum were slower than those in air by a factor of 3 to 4, the low ‡K value structure sensitive rates were slower than the air ones by at least three orders of magnitude. A hypothesis is proposed to explain this in terms of a propagation mechanism for the structure sensitive mode of fatigue crack growth.
105 citations
01 Mar 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, the authors measured the rate of fatigue crack propagation for Ti-6Al-6V-2Sn and Ti- 6 A1-4V in aqueous environments.
Abstract: The rate of fatigue crack propagation for Ti-6Al-6V-2Sn and Ti-6 A1-4V in aqueous environments has been measured as a function of solution chemistry, frequency, and stress wave form. Depending on the specific encironment, three types of fatigue crack growth rate behavior have been observed as a function of frequency. Crack growth rates increase with decreasing frequency in distilled water, while addition of Na2SO4 produces frequency-independent behavior. In solutions containing chloride or bromide ions, a reversal in frequency-dependence takes place at ΔKscc. Below this transition ΔK level, crack growth rates decrease with decreasing frequency due to passive film formation at the crack tip. Above ΔKscc corrosion fatigue crack growth is due to SCC under cyclic loading. The ΔK transition in fatigue is lower than the static stress corrosion threshold because of repeated rupture of the passive film at the crack tip, approaching KIsco only for very slow cycling frequencies.
93 citations
TL;DR: In this article, the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6Al-4V alloy.
Abstract: The importance of delay, or retardation in the rate of fatigue crack growth, produced by load interactions in variable amplitude loading on the accurate prediction of fatigue lives of engineering structures has been well recognized for some time. Heretofore, only a few simple loading combinations or spectra have been examined systematically. In this investigation the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6Al-4V alloy. The results are used to estimate crack growth behavior under programmed loads.
90 citations
TL;DR: In this article, the influence of intermittent overloads on fatigue crack growth in polymethylmethacrylate, a transparent polymer, was investigated and it was found that a significant tensile load was required to displace the portions of the crack surfaces which were initially closed.
TL;DR: In this article, an empirical crack growth rate model based on the change in crack extension force, Δℷ, was proposed and its relation to current ΔK models is discussed and observations on the fatigue surface morphology presented.
TL;DR: In this article, the authors investigated the link between the load required to open a crack at its tip and the shift in crack growth rate curves with stress ratio and found that the physical basis for the Rent can be adequately explained in terms of crack tip closure.
Abstract: Following the crack closure studies of Elber, experiments were performed which appear to corroborate the link between the load required to open a crack at its tip and the shift in crack growth rate curves with stress ratio. Measurements of fatigue crack growth rates and closure loads were made on compact tension specimens for positive stress ratios of R=0.08 to R=0.8 and at rates between 10 - 7 and 10 - 5 in./cycle. An R c u t exists for 2219-T851 and recrystallization annealed Ti-6A1-4V wherein da/dN versus ΔK data does not shift to faster rates with increasing stress ratios above R=0.32 and R=0.35, respectively. The physical basis for the Rent can be adequately explained in terms of crack tip closure. Fatigue S-N data also exhibited an R c u t when replotted as ΔS-N.
01 Jul 1974
TL;DR: In this article, single tensile overloads were applied to 4340 steel specimens which were treated to give 120 and 220 ksi yield strength levels, and the influence of yield strength level on the number of nonsteady state crack growth cycles subsequent to the application of a 100 percent overload was noted to be substantial.
Abstract: : Single tensile overloads were applied to 4340 steel specimens which were treated to give 120 and 220 ksi yield strength levels. The influence of yield strength level on the number of nonsteady state crack growth cycles subsequent to the application of a 100 percent overload was noted to be substantial. The number of nonsteady state cycles for the 120 ksi strength steel was approximately an order of magnitude greater than that of the higher strength steel. A retardation model was developed using a residual stress intensity factor concept similar to that proposed by Willenborg et al. The model was found to predict to within 10 percent the number of nonsteady state crack growth cycles required to move a crack from the pre-overload position to a subsequent position, one overload induced plane stress plastic zone radius ahead of the pre-overload position. The model indicates that the reason for substantial increase in nonsteady state crack growth cycles observed for the low strength steel is due to a corresponding increase in the overload affected zone size.
TL;DR: In this article, the effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied and the authors derived the fatigue crack propagation relation da/dN = f(R) Delta K squared with three assumptions: small-scale yielding, material homogeneity, and that crack tip stresses and strains are not strongly affected by plate thickness.
Abstract: The fatigue crack propagation relation da/dN = f(R) Delta K squared can be derived with three assumptions: small-scale yielding, material homogeneity, and that crack tip stresses and strains are not strongly affected by plate thickness. The function f(R) is a constant at a given stress ratio, R. The effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied. High Delta K level in a thin specimen causes crack tip necking. Necking is more pronounced at high stress ratio. Necking causes high maximum strain near a crack tip and fast crack growth rate.
TL;DR: In this article, the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length.
01 Jul 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, cyclic crack propagation rates for a 65 pct nickel-33 pct copper alloy in low pressure, 0.013 MPa (100 torr), environments of hydrogen, oxygen and nitrogen gas were compared to a reference crack propagation rate in a 1.3µPa vacuum.
Abstract: Cyclic crack propagation rates for a 65 pct nickel-33 pct copper alloy in low pressure, 0.013 MPa (100 torr), environments of hydrogen, oxygen, and nitrogen gas were compared to a reference crack propagation rate in a 1.3µPa vacuum. Crack propagation rates were determined over a range of temperatures for vacuum and hydrogen gas at a constant cyclic stress intensity. Crack propagation in the gaseous environment results in an increased crack propagation rate compared to growth rates in vacuum and a unique fracture mor-phology for each environment. Parallel investigations using transmission electron microscopy showed a unique dislocation structure adjacent to the fracture surface corre-sponding to each fracture morphology and environment. Fracture modes were transgran-ular in vacuum and nitrogen gas, transgranular with crystallographically-oriented features in oxygen gas, and intergranular over a range of temperature in hydrogen. A mechanism is suggested to explain gaseous environmental effects based on dislocation-gas atom inter-action.
TL;DR: In this paper, the effect of mean stress on fatigue crack propagation and on the critical fatigue crack size associated with sudden fast fracture in center-notched plate specimens of a rail steel under pulsating loading was studied.
TL;DR: In this paper, the Elber closure model was applied to HP-9Ni-4Co-30C steel heat treated to three strength levels and it was concluded that the constant amplitude crack growth rate is dependent on the strength level of the material.
01 Dec 1974
TL;DR: In this paper, the influence of alternating and mean stress intensity on fatigue crack propagation in metals has been studied in relation to the different microstructure, mean (or maximum) stress intensity and specimen thickness, particularly in the range of medium and high growth rates.
Abstract: The influence of alternating and mean stress intensity on fatigue crack propagation in.metals has been studied in relation to the different microstructure, mean (or maximum) stress intensity and specimen thickness, particularly in the range of medium and high growth rates. The simple growth law
TL;DR: In this paper, a series of experiments have been conducted to determine the effect of loading variables such as cyclic frequency, load ratio, and material on acoustic emission from fatigue-crack propagation.
Abstract: A series of experiments has been conducted to determine the effect of loading variables such as cyclic frequency, load ratio, and material on acoustic emission from fatigue-crack propagation. It is shown that the applied-stress intensity range (ΔK) is the controlling parameter for all materials studied while the other parameters have lesser effects. Two potential methods for engineering application of acoustic emission during fatigue loading are described.
TL;DR: In this article, the effect of single peak overloads on fatigue crack growth was investigated using center crack sheet specimens of 2024-T3 aluminum alloy, and a relationship was developed for approximating the amount of fatigue crack delay incurred due to overloading.
Abstract: The effect of single peak overloads on fatigue crack growth was investigated using center crack sheet specimens of 2024-T3 aluminum alloy. The magnitudes of the overload stress intensity values were selected to provide ratios of the overload plastic zone size to the fatigue plastic zone size (r0/r/max = #*) equal to 5, 10, 15, and 20. To provide a constant fatigue plastic zone size, quasi-constant stress intensity tests were run by means of a load shedding technique. The delaying effect due to a single peak overload was found to increase as the value of R* and consequently as r0, increased. The higher values of R* were large enough to produce an overload plastic zone that would result in nonpropagating fatigue cracks after 1.5 x 10 cycles. A "zeroing in" technique was used to determine the size of the plastic zone required to arrest a crack at any particular fatigue stress intensity level. From the experimental data, a relationship was developed for approximating the amount of fatigue crack delay incurred due to overloading.
TL;DR: In this article, the growth rates of Types 316 and 321 stainless steel were studied as a function of stress intensity, temperature, relative humidity, and gas environment at 25°C.
Abstract: Fatigue crack growth rates of Types 316 and 321 stainless steel were studied as a function of stress intensity, temperature, relative humidity, and gas environment At 25°C it was shown tha
TL;DR: In this article, the authors show that cyclic prestress increases subsequent fatigue crack growth rate in 2024-T351 aluminum alloy, and this increase in growth rate, caused by the prestress, and the increased rate caused by temper embrittlement as observed by Ritchie and Knott (1973), cannot be explained by the crack tip blunting model alone.
01 Sep 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, a simple model is adapted to explain the interaction of the growth rate with compressive residual stresses generated at the tip of the propagating crack, which emphasizes the interaction between the growth rates and residual stresses.
Abstract: Measurements of fatigue crack growth rates in copper monocrystalline and polycrystalline sheet specimens have been made at 295 K and 77 K to determine mean stress effects on growth rates. When load conditions remained unchanged throughout the period of crack growth, the rate of fatigue crack growth is independent of the level of mean stress and depends only on the cyclic stress amplitude. When the mean stress is changed during the crack growth period, a reduction of mean stress under plane strain conditions causes complete cessation of growth. A similar effect was not observed in plane stress crack growth, presumably due to reduced elastic constraint in narrow specimens containing large cracks. No change in growth rates occurs if the mean load is increased. In the event of crack growth stoppage, either restoration of the full previous mean load or crack re-nucleation under continued cycling at the reduced load levels is sufficient to restore the prior growth rate. A simple model is adapted to explain these observations which emphasizes the interaction of the growth rate with compressive residual stresses generated at the tip of the propagating crack.
TL;DR: In this article, a test procedure is outlined by which the rate of fatigue crack growth over a range of stress ratios and stress intensities can be determined expeditiously using a small number of specimens.
Abstract: A test procedure is outlined by which the rate of fatigue crack growth over a range of stress ratios and stress intensities can be determined expeditiously using a small number of specimens. This procedure was developed to avoid or circumvent the effects of load interactions on fatigue crack growth, and was used to develop data on a mill annealed Ti-6Al-4V alloy plate. Experimental data suggest that the rates of fatigue crack growth among the various stress ratios may be correlated in terms of an effective stress intensity range at given values of K max. This procedure is not to be used, however, for determining the corrosion fatigue crack growth characteristics of alloys when nonsteady-state effects are significant.
01 May 1974
TL;DR: In this article, a combined experimental and analytical study was undertaken to investigate the fatigue crack growth behavior of surface flaws and part-thru and thru cracks originating at fastener holes, and three alloys (2219-T851 aluminum, 9Ni-4Co-0.2C steel, and 6Al-4V (ELI) beta annealed titanium) were tested under three different loading profiles.
Abstract: : The combined experimental and analytical study was undertaken to investigate the fatigue crack growth behavior of surface flaws and part-thru and thru cracks originating at fastener holes. Three alloys (2219-T851 aluminum, 9Ni-4Co-0.2C steel, and 6Al-4V (ELI) beta annealed titanium) were tested under three different loading profiles (constant cyclic load, periodic overload, spectrum load). Surface flaw test variables included loading conditions (uniform tension, pure bending, combined bending and tension), stress ratio (0. 1, 0.3, 0.5), initial flaw shape (0.15 < a/2c < 0.45), and initial flaw depth (0.2 < a/t < 0.8). Fastener hole flaw variables included hole condition (conventional reamed and cold worked), fastener type (close tolerance and Taper- lok), and initial crack shape (uniform thru the thickness and quarter circular part-thru). All tests were conducted in air having a relative humidity of about 10 percent.